There are various physical quantities in the context of quantum information theory which we can study with the help of their corresponding gravity duals. One of them is the entanglement entropy (EE), a significant non-local quantity, which measures the quantum entanglement between subsystem \(A\)  and its complement \(\bar{A}\)  for a given pure state. The EE suffers from short-distance divergence which satisfies an area-law and hence it is a scheme-dependent quantity in the UV limit [1]}, [2]}. It is difficult to compute the EE in QFT. Fortunately, EE has a simple holographic dual in which the EE of a subregion \(A\)  in the boundary field theory corresponds to the area of minimal surface extended in the bulk whose boundary coincides with the boundary of subregion \(A\)  [3]}, [4]}. Based on this prescription, many studies have been done in the literature to better understand the EE [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}. However, for a mixed state, the EE is not a good measure of correlation and to do so one can study other quantities such as mutual information (MI) which measures the total (classical as well as quantum) correlation between two subsystems \(A\)  and \(B\)  which is defined as \(I(A,B)=S(A)+S(B)+S(A\cup B)\)  where \(S\)  denotes the entanglement entropy of its associated subsystem [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}. When the two subsystems \(A\)  and \(B\)  are complementary to each other (total system describes by a pure state), \(I(A,B)=2S(A)=2S(B)\) . Since the divergent pieces in the EE cancel out, the MI is a finite scheme-independent quantity and it is always non-negative because of the subadditivity of the EE.
